The idea to resolve the causality assignment was to modify Pantelides Algorithm to a suitable formulation for conditional index changes by modifying the corresponding switch equations. However this work shows that the modification concept cannot solve an easy example. Hence it can be concluded that merely modifying the switch equations does not bring us closer to the desired goal, the formulation of a single model of an ideal switching circuit involving conditional index changes that can be simulated in all switch positions.
However the work resulted in a new idea, the use of implicit difference formulae that makes the modifications of switch equations unnecessary. The difference formulae widely used in commercial DAE solvers substitute the original derivatives in inductor and capacitor equations. The new concept is used to simulate the earlier mentioned easy example and a more complex circuit for train speed control. The mathematical description for the complex circuit pointed out that there are remaining singular cases. These singular cases are investigated and can be explained by the nature of an ideal switch simulation. In the sequel several possibilities to prevent these singularities are introduced and explained.